Subdivision Modifier Inconsistency (2.8 stable)
After some playing around I've found the problem.

With face select mode enabled, I noticed that each edge had what appeared to be a face on it, shown by the centre dot markers normally seen in face select mode




Deleting those faces alone didn't make much difference, but with vertex select mode back on, I found that there were now twice the number of vertices than the other corners.  Merging those together with Vertex &gt; Merge Vertices &gt; By Distance solved the issue.

The mesh looks wierd on all four corners now, but that's expected and now I can fix it the normal way.